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poset game

vr.tr.poset-game · thing-q7233029

Let an agent explain poset games and their rules, identify classic examples, relay known results on winning strategies and complexity with attribution, and separate poset games from other combinatorial games.

Thing Registry Cross-cutting context XCT.REL
Bundle → Layer → Finding → QuestionsClassifiersWhat it isWhy it existsDistinguishing featuresWhat robots and AI may and may not doMoral aspectsOwnersLinks to other meta-modelsIdentity and identifiersDirect propertiesRecognitionCapabilities and actionsHazards and failure modesStandards and interfacesContext of useSources

Bundle → Layer → Finding → Questions Filled

4 bundles · 8 layers · 8 findings · 16 questions

Rules How poset games work.

Play

Rules.

Play

Play.

  1. What are the rules of a poset game, and who wins? definition
  2. Is the game a poset game or another impartial game? boundary

Examples

Classic examples.

Examples

Examples.

  1. How are Nim, Chomp and Hackendot poset games? definition
  2. Which entry fits Chomp? action
Results Known results.

Strategy

Strategy stealing.

Strategy

Strategy.

  1. Why does the first player win on posets with a greatest element, and what does strategy stealing show? provenance
  2. What is proven versus constructive? boundary

Solved

Solved cases.

Solved

Solved.

  1. Which poset games are fully solved, and how? provenance
  2. Which references are standard? provenance
Complexity Computational complexity.

Hardness

Hardness results.

Hardness

Hardness.

  1. What is known about the complexity of deciding poset games? provenance
  2. Which entry fits computational complexity? action

Algorithms

Computing outcomes.

Algorithms

Algorithms.

  1. How are outcomes computed for small posets? action
  2. What are the limits? measurement
Context History and teaching.

History

Origins.

History

History.

  1. How did poset games develop from Nim and Chomp to the general theory? provenance
  2. Which entry fits combinatorial game theory? action

Teach

Teaching.

Teach

Teaching.

  1. How are poset games used in teaching? action
  2. Which misconceptions arise? provenance

Classifiers Filled

Family
Thing Registry
Category
Cross-cutting context
Entry kind
thing
Plane
XCT
Domain
XCT.REL

What it is Filled

A two-player impartial game played on a partially ordered set in which players alternately choose an element and remove it together with every element greater than it, the player unable to move losing under normal play; poset games include Nim, Chomp and Hackendot, and deciding the winner is hard in general although special cases are solved.

Why it exists Filled

Let an agent explain poset games and their rules, identify classic examples, relay known results on winning strategies and complexity with attribution, and separate poset games from other combinatorial games.

Distinguishing features Filled

  • Played on a partial order
  • Upward removal rule
  • Impartial and finite
  • Includes Nim and Chomp

What robots and AI may and may not do Filled

Must not

  • Claim an explicit winning strategy where only its existence is proven.
  • Confuse normal play with misere play.
  • Overstate what is known about the complexity of general poset games.
  • Present a computed result for small cases as a general theorem.

Only with a human decision

  • Publishing a claimed new result as proven.

May

  • Explain the rules of poset games and examples such as Chomp and Nim.
  • Compute winning positions for small games and show the reasoning.

Moral aspects Filled

  • Honest statements about what is proven protect students and the research record.

Who is affected

  • Students of combinatorics
  • Researchers

Owners Filled

Steward

Nobody owns the concept; it belongs to the shared body of mathematics.

Links to other meta-models Filled

parent

  • Q11371326 - registry parent class

related

  • finite two-player zero-sum game - game classification
  • Chomp - a classic example
  • Nim - a special case
  • combinatorial game theory - the field

What else AI and robots need to interact with it Filled

Identity and identifiers required Filled

  • Vercy registry: vr.tr.poset-game
  • Wikidata: Q7233029 (https://www.wikidata.org/wiki/Q7233029)

Direct properties not applicable Not applicable

Not applicable

Plane XCT: no invented physical properties.

Recognition optional Filled

  • Remove an element and everything above it
  • Normal play convention
  • Games with other removal rules are outside the family
  • Not visible; a game on a diagram of an ordered set.

Capabilities and actions required Filled

  • explain the rules and examples
  • relay known results and strategy-stealing arguments
  • relay complexity results
  • distinguish from other game families

Hazards and failure modes required Filled

  • Assuming a known strategy where only existence is proven
  • Confusing misere and normal play
  • Overstating solved cases

Standards and interfaces required Filled

  • No regulation; definitions follow the research literature

Context of use required Filled

  • Not for anything; a family of games studied in combinatorial game theory.
  • Nim as a poset game on disjoint chains
  • Chomp on a grid
  • Hackendot on trees
  • divisor games and subset games
  • poset games on general orders

Sources Filled

  1. Wikidata item Q7233029: poset game - identity and sense of the item
  2. Wikipedia: Poset game - general description of the item

Open questions

  • Should Chomp and Nim be separate entries?
  • How should complexity results be linked?
  • Which open problems, such as explicit Chomp strategies, should be recorded?

Machine files

Card as JSON Specification Card backlog vercy.card/1

Provenance

thing registry research (pass 2) · unreviewed

Built from: models/things/publications/thing-q7233029/spec.json